Recently Leutheusser and Liu [1,2] identified an emergent algebra of Type III$_1$ in the operator algebra of ${\mathcal N}=4$ super Yang-Mills theory for large $N$. Here we describe some $1/N$ corrections to this picture and show that the emergent Type III$_1$ algebra becomes an algebra of Type II$_\infty$. The Type II$_\infty$ algebra is the crossed product of the Type III$_1$ algebra by its modular automorphism group. In the context of the emergent Type II$_\infty$ algebra, the entropy of a black hole state is well-defined up to an additive constant, independent of the state. This is somewhat analogous to entropy in classical physics.
This chapter discusses Edwards' early work trying to devise a convenient description of topological constraint in order to study the statistical physics of cross-linked polymers, which is related to modern descriptions of topological knots.
The Feynman $i\varepsilon$ is an important ingredient in defining perturbative scattering amplitudes in field theory. Here we describe its analog in string theory. Roughly one takes the string worldsheet to have Lorentz signature when a string is going on-shell although it has Euclidean signature generically.
We consider the deep inelastic structure functions of the photon in an asymptotically free gauge theory. In contrast to the case of a hadronic target, we find that the shortdistance analysis determines the shape and magnitude and not merely the Q 2 dependence of the structure functions. The structure functions of the free quark theory are renormalized by finite, calculable factors. For example, at x = 0.1, we find that F 2 will, at large Q 2, exceed the free quark result by a factor 1.751, while for x = 0.5, F 2 is suppressed asymptotically, relative to the free quark theory, by a factor 0.964, and at x = 0.8, by a factor 0.611.
Three subjects are considered here: a self-dual non-critical string that appears in Type IIB superstring theory at points in ${\rm K3}$ moduli space where the Type IIA theory has extended gauge symmetry; a conformal field theory singularity at such points which may signal quantum effects that persist even at weak coupling; and the rich dynamics of the real world under compactification, which may be relevant to some attempts to explain the vanishing of the cosmological constant.
By exploiting standard facts about $N=1$ and $N=2$ supersymmetric Yang-Mills theory, the Donaldson invariants of four-manifolds that admit a Kahler metric can be computed. The results are in agreement with available mathematical computations, and provide a powerful check on the standard claims about supersymmetric Yang-Mills theory.
No abstract is provided for this article.
Extending previous work that involved D3-branes ending on a fivebrane with $${\theta_{\mathrm{YM}}\neq 0}$$ , we consider a similar two-sided problem. This
No abstract is provided for this article.
It is shown that in string theory mirror duality is a gauge symmetry (a Weyl transformation) in the moduli space of N = 2 backgrounds on group manifolds, and we conjecture on the possible generalization to other backgrounds, such as Calabi-Yau manifolds.
No abstract is provided for this article.
Recently, it has been proposed by Maldacena that large $N$ limits of certain conformal field theories in $d$ dimensions can be described in terms of supergravity (and string theory) on the product of $d+1$-dimensional $AdS$ space with a compact manifold. Here we elaborate on this idea and propose a precise correspondence between conformal field theory observables and those of supergravity: correlation functions in conformal field theory are given by the dependence of the supergravity action on the asymptotic behavior at infinity. In particular, dimensions of operators in conformal field theory are given by masses of particles in supergravity. As quantitative confirmation of this correspondence, we note that the Kaluza-Klein modes of Type IIB supergravity on $AdS_5\times {\bf S}^5$ match with the chiral operators of $\N=4$ super Yang-Mills theory in four dimensions. With some further assumptions, one can deduce a Hamiltonian version of the correspondence and show that the $\N=4$ theory has a large $N$ phase transition related to the thermodynamics of $AdS$ black holes.
A long-standing puzzle about the heterotic string has been what happens when an instanton shrinks to zero size. It is argued here that the answer at the quantum level is that an extra SU(2) gauge symmetry appears that is supported in the core of the instanton. Thus in particular the quantum heterotic string has vacua with higher rank than is possible in conformal field theory. When k instantons collapse at the same point, the enhanced gauge symmetry is Sp(k). These results, which can be tested by comparison to Dirichlet five-branes of Type I superstrings and to the ADHM construction of instantons, give the first example for the heterotic string of a non-perturbative phenomenon that cannot be turned off by making the coupling smaller. They have applications to several interesting puzzles about string duality.
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The supersymmetric string of Schwarz and Green [1] is a variant of the old fermionic string theory of Ramond-Neveu-Schwarz [2]. It is consistent only in ten dimensions and apparently must be interpreted in the sense of a Kaluza-Klein theory, the ten dimensions consisting of four Minkowskian ones and six compact ones.
In toroidal compactification of string theory, enlarged symmetry groups arise at special radii of the compactified dimensions. Here an orbifold-like construction is considered in which the degrees of freedom describing the compact spatial dimensions are twisted by symmetries which exist only for special values of the radius. Constraints on the possible twists arising from the requirements of worldsheet supersymmetry and modular invariance are described, and some simple examples are given. One motivation for this work is that in twisting by a symmetry which exists only at a special value of the radius, one of the dilaton-like fields can acquire a mass, since the radius of the compact space is fixed.
